Abstract
We describe the contribution of diffractive orbits to semiclassical approximations of Wigner function propagators. These contributions are based on diffractively scattered rays used in the geometrical theory of diffraction (GTD). They provide an extension of well-established approximations of Wigner-function propagators based on rays that propagate by specular reflection and refraction. The wider aim of this approach is to allow for diffractive mechanisms to be accounted for in Eulerian approaches to ray-tracing simulations. Such approaches propagate densities of rays rather than follow rays individually. They promise to be a more efficient means of performing ray-tracing simulations in complex environments with applications in, for example, planning of wireless signal coverage for mobile communication networks.
Highlights
Accounting for diffraction is a vital part of planning radio coverage in large-scale, complex environments
We describe the contribution of diffractive orbits to semiclassical approximations of Wigner function propagators
Diffractive mechanisms are routinely incorporated into ray-tracing simulations of radio coverage [2] using developments of the geometrical theory of diffraction (GTD) [3] and the uniform theory of diffraction (UTD) [4]
Summary
Accounting for diffraction is a vital part of planning radio coverage in large-scale, complex environments. Modelling of radio coverage is best tackled using ray tracing methods [1]: the aim of this paper is to allow diffractive mechanisms to be more efficiently incorporated into such phase-space simulations by calculating diffractive contributions to propagators of Wigner functions. In this paper we provide a means of incorporating diffractive rays into an Eulerian approach, that is, an approach where the propagation of power is modelled in terms of a phase-space density rather than by following individual rays This can lead to efficiency gains in multiplescattering scenarios, such as modelling indoor wireless coverage where losses are typically low and multiple reflections dominate. Full electromagnetic wave calculations in multiple scattering environments typically show strong fluctuations due to the interference between multiple paths of propagation, which may be approximated by summing over ray pairs satisfying appropriate boundary conditions [13, 17] Implementing such schemes in full in a complex environment is a computationally challenging task.
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